Abbreviations - International Monetary Fund

Producer Price Index Manual The exposition in this chapter does not therefore follow the same order as the chapters in the Manual. 1.7 The main topics covered in this chapter are as follows: The uses and origins of PPIs; Basic index number theory, including the axiomatic and economic approaches to PPIs; Elementary price indices and aggregate PPIs; The transactions, activities, and establishments covered by PPIs; The collection and processing of the prices, including adjusting for quality change; The actual calculation of the PPI; Potential errors and bias; Organization, management, and dissemination policy; and An appendix providing an overview of the steps necessary for developing a PPI. 1.8 Not all of the topics treated in the Manual are included in this chapter. The objective of this general introduction is to provide a summary presentation of the core issues with which readers need to be acquainted before tackling the detailed chapters that follow. It is not the purpose of this introduction to provide a comprehensive summary of the entire contents of the Manual. Some special topics, such as the treatment of certain products whose prices cannot be directly observed, are not considered here because they do not affect general PPI methodology. A. The Uses and Origins of PPIs 1.9 Four of the principal price indices in the system of economic statistics—the PPI, the CPI, and the export and import price indices—are well known and closely watched indicators of macroeconomic performance. They are direct indicators of the purchasing power of money in various types of transactions and other flows involving goods and services. As such, they are also used to deflate nominal measures of goods and services produced, consumed, and traded to provide measures of volumes. Consequently, these indices are important tools in the design and conduct of the monetary and fiscal policy of the government, but they are also of great utility in informing economic decisions throughout the private sector. They do not, or should not, comprise merely a collection of unre4 lated price indicators but provide instead an integrated and consistent view of price developments pertaining to production, consumption, and international transactions in goods and services. 1.10 In the system of price statistics, PPIs serve multiple purposes. The precise way in which they are defined and constructed can very much depend on by whom and for what they are meant to be used. PPIs can be described as indices designed to measure the average change in the price of goods and services either as they leave the place of production or as they enter the production process. A monthly or quarterly PPI with detailed product and industry data allows monitoring of short-term price inflation for different types or through different stages of production. Although PPIs are an important economic indicator in their own right, a vital use of PPIs is as a deflator of nominal values of output or intermediate consumption for the compilation of production volumes and for the deflation of nominal values of capital expenditure and inventory data for use in the preparation of national accounts.1 1.11 Beyond their use as inflationary indicators or as deflators, certain frameworks for PPIs provide insight into the interlinkages between different price measures. One such framework is aggregation of stage-of-processing indices. This concept classifies goods and services according to their position in the chain of production—that is, primary products, intermediate goods, and finished goods. This method allows analysts to track price inflation through the economy. For example, changes in prices in the primary stage could feed through into the later stages, so the method gives an indicator of future inflation further down the production chain. However, each product is allocated to only one stage in the production chain even though it could occur in several stages. This topic will be considered in Chapter 2 and again in Chapter 14. 1.12 A further method for analysis is to aggregate by stage of production, in which each product is allocated to the stage in which it is used. This differs from stage of processing because a product is included in each stage to which it contributes and is not assigned solely to one stage. The classification of products to the different stages is usually 1 PPIs are used for this purpose because the volumes underlying the nominal values are not directly measurable.

1. An Introduction to PPI Methodology achieved by reference to input-output tables, and, in order to avoid multiple counting, the stages are not aggregated. There is a growing interest in this type of analysis. For example, these types of indices are already compiled on a regular basis in Australia.2 This topic will also be considered in Chapters 2 and 14. 1.13 As explained in Chapter 2, PPIs have their beginnings in the development of the wholesale price index (WPI) dating back to the late 19th century. Laspeyres and Paasche indices, which are still widely used today, were first proposed in the mid19th century. They are explained below. The concepts of the fixed-input output price index and the fixed-output input price index were introduced in the mid- to late 20th century. These two concepts provide the basic framework for the economic theory of the PPI presented in Chapters 15 and 17. 1.14 Initially, one of the main reasons for compiling a WPI was to measure price changes for goods sold in primary markets before they reached the final stage of production at the retail market level. Thus the WPI was intended to be a general purpose index to measure the price level in markets other than retail. The WPI has been replaced in most countries by PPIs because of the broader coverage provided by the PPI in terms of products and industries and the conceptual concordance between the PPI and the System of National Accounts, discussed in more detail in Chapter 14. It is this concordance that makes components of the PPI useful as deflators for industrial outputs and product inputs in the national accounts. In addition, the overall PPI and PPIs for specific products are used to adjust prices of inputs in long-term purchase and sales contracts, a procedure known as “escalation.” 1.15 These varied uses often increase the demand for PPI data. For example, using the PPI as an indicator of general inflation creates pressure to extend its coverage to include more industries and products. While many countries initially develop a PPI to cover industrial goods produced in mining and manufacturing industries, the PPI can logically be extended to cover all economic activities, as noted in Chapters 2 and 14. B. Some Basic Index Number Formulas 1.16 The first question is to decide on the kind of index number to use. The extensive list of references given at the end of this Manual reflects the large literature on this subject. Many different mathematical formulas have been proposed over the past two centuries. Nevertheless, there is now a broad consensus among economists and compilers of PPIs about what is the most appropriate type of formula to use, at least in principle. While the consensus has not settled for a single formula, it has narrowed to a very small class of superlative indices. A characteristic feature of these indices is that they treat the prices and quantities in both periods being compared symmetrically. They tend to yield very similar results and behave in very similar ways. 1.17 However, when a monthly or quarterly PPI is first published, it is invariably the case that there is not sufficient information on the quantities and revenues in the current period to make it possible to calculate a symmetric, or superlative, index. It is necessary to resort to second-best alternatives in practice, but in order to be able to make a rational choice between the various possibilities, it is necessary to have a clear idea of the target index that would be preferred, in principle. The target index can have a considerable influence on practical matters such as the frequency with which the weights used in the index should be updated. 1.18 The Manual provides a comprehensive, thorough, rigorous, and up-to-date discussion of relevant index number theory. Several chapters from Chapter 15 onward are devoted to a detailed explanation of index number theory from both a statistical and an economic perspective. The main points are summarized in the following sections. Many propositions or theorems are stated without proof in this chapter because the proofs are given or referenced in later chapters to which the reader can easily refer in order to obtain full explanations and a deeper understanding of the points made. There are numerous cross-references to the relevant sections in later chapters. 2 See, for example, Australian Bureau of Statistics (ABS) (2003 and other years); available via the Internet: www.abs.gov.au. 5

Producer Price Index Manual B.1 Price indices based on baskets of goods and services year, whereas the index may be compiled monthly or quarterly. 1.19 The purpose of an index number may be explained by comparing the values of producer’s revenues from the production of goods and services in two time periods. Knowing that revenues have increased by 5 percent is not very informative if we do not know how much of this change is due to changes in the prices of the goods and services and how much to changes in the quantities produced. The purpose of an index number is to decompose proportionate or percentage changes in value aggregates into their overall price and quantity change components. A PPI is intended to measure the price component of the change in producer’s revenues. One way to do this is to measure the change in the value of an aggregate by holding the quantities constant. 1.22 Let there be n products in the basket with prices pi and quantities qi. Let period b be the period to which the quantities refer and periods 0 and t be the two periods whose prices are being compared. In practice, it is invariably the case that b 0 t when the index is first published, and this is assumed here. However, b could be any period, including one between 0 and t, if the index is calculated some time after t. The Lowe index is defined in equation (1.1). B.1.1 Lowe indices 1.20 One very wide, and popular, class of price indices is obtained by defining the index as the percentage change between the periods compared in the total cost of producing a fixed set of quantities, generally described as a “basket.” The meaning of such an index is easy to grasp and to explain to users. This class of index is called a Lowe index in this Manual, after the index number pioneer who first proposed it in 1823: see Section B.2 of Chapter 15. Most statistical offices make use of some kind of Lowe index in practice. It is described in some detail in Sections D.1 and D.2 of Chapter 15. 1.21 In principle, any set of goods and services could serve as the basket. The basket does not have to be restricted to the basket actually produced in one or other of the two periods compared. For practical reasons, the basket of quantities used for PPI purposes usually has to be based on a survey of establishment revenues conducted in an earlier period than either of the two periods whose prices are compared. For example, a monthly PPI may run from January 2000 onward, with January 2000 100 as its price reference period, but the quantities may be derived from an annual revenue survey made in 1997 or 1998, or even spanning both years. Because it takes a long time to collect and process revenue data, there is usually a considerable time lag before such data can be introduced into the calculation of PPIs. The basket may also refer to a 6 n (1.1) PLo pq i 1 n t i b i p q i 1 where si0b 0 b i i n ( pit pi0 ) si0b , i 1 pi0 qib n pi0 qib . i 1 The Lowe index can be written, and calculated, in two ways: either as the ratio of two value aggregates, or as an arithmetic weighted average of the price ratios, or price relatives, pit / pi0, for the individual products using the hybrid revenue shares si0b as weights. They are described as hybrid because the prices and quantities belong to two different time periods, 0 and b, respectively. The hybrid weights may be obtained by updating the actual revenue shares in period b, namely pibqib / pibqib, for the price changes occurring between periods b and 0 by multiplying them by the price relative between b and 0, namely pi0 / pib. The concept of the base period is somewhat ambiguous with a Lowe index, since either b or 0 might be interpreted as being the base period. To avoid ambiguity, b is described as the weight reference period and 0 as the price reference period. 1.23 Lowe indices are widely used for PPI purposes. B.1.2 Laspeyres and Paasche indices 1.24 Any set of quantities could be used in a Lowe index, but there are two special cases that figure prominently in the literature and are of considerable importance from a theoretical point of view. When the quantities are those of the first of the two periods whose prices are being compared—

1. An Introduction to PPI Methodology that is, when b 0—the Laspeyres index is obtained, and when quantities are those of the second period—that is, when b t,—the Paasche index is obtained. It is necessary to consider the properties of Laspeyres and Paasche indices, and also the relationships between them, in more detail. 1.25 The formula for the Laspeyres price index, PL, is given in equation (1.2). n (1.2) PL pq i 1 n t i 0 i p q i 1 0 0 i i n ( pit pi0 ) si0 , i 1 where si0 denotes the share of the value of product i in the total output of goods and services in period 0: that is, pi0 qi0 / pi0 qi0 . 1.26 As can be seen from equation (1.2), and as explained in more detail in Chapter 15, the Laspeyres index can be expressed in two alternative ways that are algebraically identical: first, as the ratio of the values of the basket of producer goods and services produced in period 0 when valued at the prices of periods t and 0, respectively; second, as a weighted arithmetic average of the ratios of the individual prices in periods t and 0 using the value shares in period 0 as weights. The individual price ratios, (pit/pi0), are described as price relatives. Statistical offices often calculate PPIs using the second formula by recording the percentage changes in the prices of producer goods and services sold and weighting them by the total value of output in the base period 0. 1.27 The formula for the Paasche index, PP, is given in equation (1.3). n pq t i t i 1 1 n (1.3) PP ( pit pi0 ) sit , pi0 qit i 1 i 1 n i 1 where sit denotes the actual share of the expenditure on commodity i in period t: that is, pitqit / pitqit. The Paasche index can also be expressed in two alternative ways, either as the ratio of two value aggregates or as a weighted average of the price relatives, the average being a harmonic average that uses the revenue shares of the later period t as weights. However, it follows from equation (1.1) that the Paasche index can also be expressed as a weighted arithmetic average of the price relatives using hybrid expenditure weights in which the quantities of t are valued at the prices of 0. 1.28 If the objective is simply to measure the price change between the two periods considered in isolation, there is no reason to prefer the basket of the earlier period to that of the later period, or vice versa. Both baskets are equally relevant. Both indices are equally justifiable, or acceptable, from a conceptual point of view. In practice, however, PPIs are calculated for a succession of time periods. A time series of monthly Laspeyres PPIs based on period 0 benefits from requiring only a single set of quantities (or revenues), those of period 0, so that only the prices have to be collected on a regular monthly basis. A time series of Paasche PPIs, on the other hand, requires data on both prices and quantities (or revenues) in each successive period. Thus, it is much less costly, and time consuming, to calculate a time series of Laspeyres indices than a time series of Paasche indices. This is a decisive practical advantage of Laspeyres (as well as Lowe) indices over Paasche indices and explains why Laspeyres and Lowe indices are used much more extensively than Paasche indices. A monthly Laspeyres or Lowe PPI can be published as soon as the price information has been collected and processed, since the base-period weights are already available. B.1.3 Decomposing current-value changes using Laspeyres and Paasche indices 1.29 Laspeyres and Paasche quantity indices are defined in a similar way to the price indices, simply by interchanging the ps and qs in formulas (1.2) and (1.3). They summarize changes over time in the flow of quantities of goods and services produced. A Laspeyres quantity index values the quantities at the fixed prices of the earlier period, while the Paasche quantity index uses the prices of the later period. The ratio of the values of the revenues in two periods (V) reflects the combined effects of both price and quantity changes. When Laspeyres and Paasche indices are used, the value change can be exactly decomposed into a price index times a quantity index only if the Laspeyres price (quantity) index is matched with the Paasche quantity (price) index. Let PL and QL denote the Laspeyres price 7

Producer Price Index Manual and quantity indices and let PP and QP denote the Paasche price and quantity indices. As shown in Chapter 15, PL QP V and PP QL V. 1.30 Suppose, for example, a time series of industry output in the national accounts is to be deflated to measure changes in output at constant prices over time. If it is desired to generate a series of output values at constant base-period prices (whose movements are identical with those of the Laspeyres volume index), the output at current prices must be deflated by a series of Paasche price indices. Laspeyres-type PPIs would not be appropriate for the purpose. B.1.4 Ratios of Lowe and Laspeyres indices 1.31 The Lowe index is transitive. The ratio of two Lowe indices using the same set of qbs is also a Lowe index. For example, the ratio of the Lowe index for period t 1 with price reference period 0 divided by that for period t also with price reference period 0 is: n (1.4) n pit 1qib i 1 n pi0 qib i 1 n pq p q i 1 t i b i i 1 n 0 b i i p i 1 n t 1 b i i pq PLot ,t 1 . b i 1.32 This is a Lowe index for period t 1, with period t as the price reference period. This kind of index is, in fact, widely used to measure short-term price movements, such as between t and t 1, even though the quantities may date back to some much earlier period b. 1.33 A Lowe index can also be expressed as the ratio of two Laspeyres indices. For example, the Lowe index for period t with price reference period 0 is equal to the Laspeyres index for period t with price reference period b divided by the Laspeyres index for period 0 also with price reference period b. Thus, n (1.5) PLo pq i 1 n b i p q i 1 8 t i 0 b i i n n pq p q i 1 n t i b i i 1 n b b i i p q p q i 1 0 b i i 1.34 It is useful to have a formula that enables a Lowe index to be calculated directly as a chain index in which the index for period t 1 is obtained by updating the index for period t. Because Lowe indices are transitive, the Lowe index for period t 1 with price reference period 0 can be written as the product of the Lowe index for period t with price reference period 0 multiplied the Lowe index for period t 1 with price reference period t. Thus, n t b n t 1 b pi qi pi qi i 1 i 1n i n 1 (1.6) n 0 b 0 b t b p q p q p q i i i i i i i 1 i 1 i 1 n t b pi qi n pt 1 i t sitb , i n 1 p 0 q b i 1 pi i i i 1 n p t 1 b i i q where the revenue weights sitb are hybrid weights defined as: q t i i 1 B.1.5 Updated Lowe indices i 1 b b i i PLt . PL0 (1.7) sitb pit qib n pq i 1 t i b i . 1.35 Hybrid weights of the kind defined in equation (1.7) are often described as price-updated weights. They can be obtained by adjusting the original revenue weights pibqib / pibqib by the price relatives pit / pib. By price updating the revenue weights from b to t in this way, the index between t

Abbreviations xxix PC Carli price index PCSWD Carruthers, Sellwood, Ward, and Dalén price index PD Dutot price index PDR Drobisch index PF Fisher price index PGL Geometric Laspeyres price index PGP Geometric Paasche price index PH Harmonic average of price relatives PIT Implicit Törnqvist price index PJ Jevons price index PJW Geometric Laspeyres price index (weighted Jevons index)